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Timetable (PFDW01)

Training Course: Pattern Formation in Large Domains

Monday 1st August 2005 to Friday 5th August 2005

Monday 1st August 2005
08:30 to 10:00 Registration INI 1
10:00 to 11:00 A Rucklidge ([Leeds])
Introductory Lecture 1: Pattern forming systems
INI 1
11:00 to 11:30 Coffee
11:30 to 12:30 P Matthews ([Nottingham])
Introductory Lecture 2: Review of dynamical systems concepts
INI 1
12:30 to 13:30 Lunch at Wolfson Court
14:00 to 15:00 M Cross ([CALTECH])
Spatially extended pattern formation 1: Stripe patterns I - basic ideas and amplitude equations
INI 1
15:00 to 16:00 Poster Advertisement
16:00 to 16:30 Tea
16:30 to 17:30 G Ahlers ([California, Santa Barbara])
Experimental illustrations of pattern-forming phenomena: Examples from Rayleigh-Benard and electro convection

Using experimental examples from Rayleigh-Benard convection and from electro convection in a nematic liquid crystal, this talk will illustrate various concepts involved in the formation of patterns in spatially extended systems.

INI 1
17:30 to 18:30 Poster session 1 and Wine reception
18:45 to 19:30 Dinner at Wolfson Court (Residents only)
Tuesday 2nd August 2005
09:00 to 10:00 M Cross ([CALTECH])
Spatially extended pattern formation 2: Stripe patterns II - symmetry and phase equations
INI 1
10:00 to 11:00 JHP Dawes ([Cambridge])
Symmetric bifurcation theory 1: Groups, representations and linear theory
INI 1
11:00 to 11:30 Coffee
11:30 to 12:30 M Cross ([CALTECH])
Spatially extended pattern formation 3: Oscillatory patterns
INI 1
12:30 to 13:30 Lunch at Wolfson Court
14:00 to 15:15 Problem class / Computer lab 1 Centre for Mathematical Sciences INI 1
15:15 to 15:45 Tea at Isaac Newton Institute
15:45 to 17:00 Problem class / Computer lab 2 Centre for Mathematical Sciences
17:00 to 18:00 R Ecke (Los Alamos National Laboratory)
Spatio-temporal dynamics in Rayleigh-Benard convection

Rayleigh-Benard convection has been a workhorse system for the precise study of phenomena in pattern formation for over 30 years. In the 1990s experiments became available in which very large aspect ratios could be obtained; ratios of lateral size to height of between 50 and 150 were realized. Further, computer acquisition allowed for the accumulation of thousands of images and their subsequent analysis using sophisticated image processing. From these advances came the extensive investigation of spatio-temporal chaos in large domains. In particular, two problems were of the greatest importance: spiral defect chaos in non-rotating convection and domain chaos in rotating convection and in electro-convection. With an emphasis on experimental results, I will review some aspects of these two spatio-temporally chaotic states and will consider unresolved questions that remain today.

INI 1
18:45 to 19:30 Dinner at Wolfson Court (Residents only)
Wednesday 3rd August 2005
09:00 to 10:00 M Cross ([CALTECH])
Spatially extended pattern formation 4: Spatiotemporal chaos
INI 1
10:00 to 11:00 JHP Dawes ([Cambridge])
Symmetric bifurcation theory 2: Amplitude equations and Hopf bifurcations
INI 1
11:00 to 11:30 Coffee
11:30 to 12:30 L Tuckerman & D Barkley ([LIMSI-CNRS/Warwick])
Numerical methods 1: Integration of partial differential equations
INI 1
12:30 to 13:30 Lunch at Wolfson Court
14:00 to 18:00 Poster session 2
18:45 to 19:30 Dinner at Wolfson Court (Residents only)
Thursday 4th August 2005
09:00 to 10:00 L Tuckerman & D Barkley ([LIMSI-CNRS/Warwick])
Numerical methods 2: Linearisation
INI 1
10:00 to 11:00 JHP Dawes ([Cambridge])
Symmetric bifurcation theory 3: From PDEs to ODEs
INI 1
11:00 to 11:30 Coffee
11:30 to 12:30 L Tuckerman & D Barkley ([LIMSI-CNRS/Warwick])
Numerical methods 3: Steady state solving and branch following
INI 1
12:30 to 13:30 Lunch at Wolfson Court
14:00 to 16:00 Problem class / Computer lab 3 Centre for Mathematical Sciences
16:00 to 16:30 Tea at Isaac Newton Institute
17:00 to 18:00 M Golubitsky ([Houston])
Pattern formation in coupled cell systems

A coupled cell system is a collection of interacting dynamical systems. Coupled cell models assume that the output from each cell is important and that signals from two or more cells can be compared so that patterns of synchrony can emerge. We show that patterns of synchrony in planar lattice dynamical systems can be very complicated, but that they are all spatially doubly periodic if enough coupling is assumed.

19:30 to 18:00 Conference Dinner at Trinity College (Old Kitchens)
Friday 5th August 2005
10:00 to 11:00 L Tuckerman & D Barkley ([LIMSI-CNRS/Warwick])
Numerical methods 4: Case studies
INI 1
11:00 to 11:30 Coffee
11:30 to 12:30 JHP Dawes ([Cambridge])
Symmetric bifurcation theory 4: Heteroclinic cycles and networks
INI 1
12:30 to 13:30 Lunch at Wolfson Court
14:00 to 16:00 Problem class / Computer lab 4 Centre for Mathematical Sciences
16:00 to 16:30 Tea at Isaac Newton Institute
17:30 to 18:00 Closing Discussion INI 1
18:45 to 19:30 Dinner at Wolfson Court (Residents only)
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons